Cell, Vol. 123, 195–205, October 21, 2005, Copyright ©2005 by Elsevier Inc. DOI 10.1016/j.cell.2005.10.001
A Structure-Based Model for
the Synthesis and Hydrolysis
of ATP by F1-ATPase
Yi Qin Gao,1,3 Wei Yang,1,3 and Martin Karplus1,2,*
1
Department of Chemistry and Chemical Biology
Harvard University
Cambridge, Massachusetts 02138
2
Laboratoire de Chimie Biophysique, ISIS
Université Louis Pasteur
67000 Strasbourg
France
Many essential functions of living cells are performed
by nanoscale protein motors. The best characterized
of these is FoF1-ATP synthase, the smallest rotary motor. This rotary motor catalyzes the synthesis of ATP
with high efficiency under conditions where the reactants (ADP, H2PO4−) and the product (ATP) are present
in the cell at similar concentrations. We present a detailed structure-based kinetic model for the mechanism of action of F1-ATPase and demonstrate the role
of different protein conformations for substrate binding during ATP synthesis and ATP hydrolysis. The
model shows that the pathway for ATP hydrolysis is
not simply the pathway for ATP synthesis in reverse.
The findings of the model also explain why the cellular concentration of ATP does not inhibit ATP synthesis.
Introduction
The motor enzyme FoF1-ATP synthase of mitochondria
uses the proton-motive force across the mitochondrial
membranes to make ATP from ADP and Pi (H2PO4−)
(Boyer, 1997; Abrahams et al., 1994; Senior et al., 2002;
Karplus and Gao, 2004). It does so under cellular conditions that favor the hydrolysis reaction by a factor of
2 × 105. In fact, as a result of the activity of the FoF1ATP synthase, the concentration ratio (ATP:ADP/Pi) is
close to unity in mitochondria (Karplus and Gao, 2004;
Nakamoto et al., 2000). This remarkable property is
based on the essential difference between an ordinary
enzyme, which increases the rate of reaction without
shifting the equilibrium, and a catalytic motor (Alberts,
1998) like FoF1-ATP synthase, which can drive a reaction away from equilibrium by harnessing an external
force. Given that a sedentary adult synthesizes and
uses about 40 kg of ATP per day (Voet and Voet, 1995),
an understanding of the detailed mechanism of FoF1ATP synthase is essential for a molecular explanation
of the biology of living cells.
FoF1-ATP synthase is composed of two domains (Figure 1): a transmembrane portion (Fo), the rotation of
which is induced by a proton gradient, and a globular
catalytic moiety (F1) that synthesizes and hydrolyzes
ATP. In this article, we focus on the F1-ATPase moiety,
for which high-resolution structures are available (Abrahams et al., 1994; Gibbons et al., 2000; Braig et al.,
2000; Menz et al., 2001; Kagawa et al., 2004). F1*Correspondence: [email protected]
3
These authors contributed equally to this work.
Theory
ATPase can synthesize, as well as hydrolyze, ATP. ATP
synthesis has been demonstrated recently by applying
an external torque to the γ subunit, causing it to rotate
in the reverse direction from that observed during ATP
hydrolysis (Itoh et al., 2004). Thus, the primary function
of the proton-motive force acting on FoF1-ATP synthase
is to provide the torque required to rotate the γ subunit
in the direction for ATP synthesis.
F1-ATPase has three α and three β subunits arranged
in alternation around the γ subunit, which has a globular
base and an extended coiled-coil domain (Abrahams et
al., 1994) (Figure 1). All of the α and β subunits bind
nucleotides, but only the three β subunits are catalytically active. The crystal structures of F1-ATPase provide views of distinct conformational states of the catalytic β subunits (Abrahams et al., 1994; Braig et al.,
2000; Menz et al., 2001; Kagawa et al., 2004). The
centrally located and asymmetric γ subunit forms a shaft,
and it has been proposed that its orientation determines the conformations of the β subunits. The original
crystal structure (Abrahams et al., 1994) of F1-ATPase
from bovine heart mitochondria led to the identification
of three conformations of the β subunit: βE (empty), βTP
(ATP analog bound), and βDP (ADP bound). In a more
recent high-resolution crystal structure (Menz et al.,
2001), the βTP and βDP subunits contain an ATP analog
(ADP plus AlF4−) and the third catalytic subunit has a
half-closed conformation, called βHC, containing ADP
plus SO4− (an analog of Pi). The open βE and half-closed
βHC conformations of the third β subunit are both very
different from those of the βTP and βDP subunits, which
are both closed and very similar to each other in all
structures. Specifically, the βHC conformation is between the “open” βE conformation, in which the interaction between β strands 3 and 7 is disrupted, and the
“closed” βTP and βDP conformations (Figure 2), in which
the nucleotide binding domain and α-helical domain
have rotated toward each other by 30° with respect to
their positions in βE (Abrahams et al., 1994).
From his insightful analysis of kinetic data, in advance of detailed structural information, Paul Boyer
proposed a “binding change mechanism” by which rotary catalysis could operate (Boyer, 1993). In a modern
interpretation of the mechanism, which differs in detail
from Boyer’s original proposal, ATP synthesis proceeds
by the cyclical conversion of each of the β subunits
from an “open” state that binds to nucleotide only
weakly to a “tight” state that has highest affinity for ATP
and finally to a “loose” state, which has a lower affinity
for ATP and from which ATP can be released. The first
crystal structure (Abrahams et al., 1994) clearly supported the general features of the binding change
mechanism, as did single-molecule experiments (Noji
et al., 1997; Yasuda et al., 1998, 2001). Researchers
were reluctant to accept the rotary mechanism until its
explicit visualization (Noji et al., 1997), but it is now generally accepted and forms the conceptual basis of the
quantitative model we present here.
Given the remarkable properties of F1-ATPase, this
rotary-motor enzyme has been the subject of many ex-
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nior, 1997; Allison, 1998), but none of them provide a
consistent and comprehensive picture of how the F1ATPase operates during both ATP hydrolysis and ATP
synthesis. This is due mostly to the lack of a quantitative description of how the thermodynamics and kinetics of the enzyme are related to the structural data.
Essential elements for developing such a mechanism
have been missing. However, recent molecular dynamics simulations have supplied the “missing link”
between the high-resolution crystal structure of F1ATPase and the measurements in solution and of single molecules.
On the basis of these results, we can now formulate
a consistent structure-based model for both ATP synthesis and hydrolysis by F1-ATPase. In developing this
model, we have sought to answer a number of essential
questions, which are listed below. We focus here on the
primary function of the F1-ATPase motor—that is, ATP
synthesis—although a corresponding model for hydrolysis is also given in the paper. For each question, we
indicate in general terms how it is resolved by our
analysis. More complete explanations are provided in
the Results and Discussion.
Figure 1. Structural Model of FoF1-ATP Synthase
The figure is from Senior et al. (2002) with permission of the author.
The F1 portion is based on the crystal structure determined by Gibbons et al. (2000), and the Fo portion is based on NMR and mutation data obtained by Rastogi and Girvin (1999). The three conformations of the β subunits in the 1BMF crystal structure (Abrahams
et al., 1994) (E1 in this paper) are called βE (empty), βTP (bound with
AMP-PNP), and βDP (bound with ADP), and the three conformations
of the β subunits in the 1H8E crystal structure (Menz et al., 2001)
(E2 in this paper) are called βHC (bound with ADP/SO42−), βTP (bound
with ADP/AlF4−), and βDP (bound with ADP/AlF4−).
perimental studies. Nevertheless, a detailed understanding of the mechanism by which it carries out its
functions is not available. Several pictorial models of
the mechanism of F1-ATPase hydrolysis have been proposed (Boyer, 1997; Menz et al., 2001; Weber and Se-
1. How Does Rotation of the g Shaft Induced Either
by the Proton-Motive Force (Boyer, 1997) or an
External Force (Itoh et al., 2004) Alter the
Conformations of the Catalytic Subunits?
The mechanism involved has been elucidated by molecular dynamics simulations (Ma et al., 2002; Böckmann and Grubmüller, 2002) and normal mode calculations of F1-ATPase (Cui et al., 2004; Sun et al., 2003).
2. What Is the Binding Affinity of Each Structurally
Defined Binding Site?
Specifically, what is the relationship between the measured solution affinities for ATP and ADP, Pi, and the
binding sites in the different conformations of the catalytic subunits observed in the X-ray structures? Answering this question is critical to generating a consistent model for the function of F1-ATPase. The answer
determines the role of the different protein conformations in the synthesis and hydrolysis of ATP. Because
Figure 2. The Structure of the βDP Site with
Bound ATP
For clarity, only the most important residues
discussed in the text are shown. The structure is based on a crystal structure (1H8E)
with ADP and AlF4− in the binding site. To
obtain the structure illustrated, the ATP was
created by overlapping the corresponding
portion with ADP, and the γ-phosphate was
superimposed on the Al atom. The system
with the ATP ligand modeled into the active
site was allowed to relax by a molecular dynamics simulation and is close to the original
crystal structure.
Theory
197
these sites exist in a single structure, measurement of
their individual binding affinities has not been possible.
This is in contrast to most other motor proteins, such
as myosin, in which separate structures with different
affinities exist in solution and in crystals. Moreover, the
βTP and βDP sites, which are bound with ligands in all
structures, have very similar conformations. Recently,
the missing link between the experimental solution
measurement and X-ray structures has been obtained
by the use of free-energy simulations (Yang et al., 2003).
The results described in this paper provide the thermodynamic basis for the structure-based model for the
synthesis and hydrolysis of ATP by F1-ATPase.
3. What Is the Mechanism by which F1-ATPase
Synthesizes ATP from ADP and Pi against
a Strong Thermodynamic Driving Force
Biased toward Hydrolysis?
Although the essential concept is contained in the
binding change mechanism of Boyer, an unresolved issue has been how the rotation of the γ subunit is coupled to the different conformations and binding affinities of the catalytic β subunits. This is now understood,
given the answers to questions 1 and 2, and is described in detail here.
4. How Does the Enzyme Avoid Being Inhibited
by ATP during ATP Synthesis When Its Concentration
Is Essentially Equal to that of ADP and Pi,
as It Is in the Mitochondria? How Is the Enzyme
Optimized for Both ATP Synthesis and Hydrolysis
as the Only Bidirectional Protein Machine in the Cell?
The thermodynamic understanding of F1-ATPase allows us to construct a kinetic model, which answers
these questions. The important realization for explaining the bidirectional functionality of F1-ATPase is that
synthesis is not the exact inverse of hydrolysis, in accord with a prescient suggestion of Senior et al. (2002).
Different catalytic subunits are involved in substrate
binding and release in synthesis and hydrolysis. This is
codified in the structure-based kinetic model, which
has the E1E2 mechanism (DeMeis and Vianna, 1979) as
one of its essential elements. In the current realization
of the E1E2 mechanism, two major protein conformations are involved, one for reactant binding and the
other for product release. ADP/Pi binding in synthesis
and release during hydrolysis involves primarily the
“half-closed” βHC site in the E2 conformation; ATP release during synthesis and binding during hydrolysis
involves primarily the open βE site in the E1 conformation. The resulting kinetic model not only provides an
interpretation of the available kinetic data but predicts
new results. It also indicates how the activity of F1ATPase is regulated in the cell as a function of the physiological concentrations of ATP, ADP, and Pi.
5. What Is the Chemical Occupancy of Each
Structurally Defined Binding Site during ATP
Synthesis and Hydrolysis?
The answer resolves whether synthesis and hydrolysis
operate through a bisite or trisite mechanism, a question that continues to be debated. By a bisite mechanism
(Boyer, 1993), we mean that, at any stage of ATP hydrolysis or synthesis, the occupation of only two catalytic
sites but not the third is required, whereas a trisite
mechanism (Senior et al., 2002) requires all three sites
to be occupied for the maximal rate of enzyme func-
tion. The analysis demonstrates that a trisite mechanism is operative when F1-ATPase is working optimally
and elucidates how the cooperativity among the catalytic subunits is achieved. The negative cooperativity of
ATP and ADP binding to the catalytic sites plays an
essential role in generating the driving force for the rotation of the γ subunit during ATP hydrolysis. In turn, the
rotation of the γ subunit leads to positive cooperativity
during catalysis. We note that rotary catalysis leads to
an increase in the observed hydrolysis rate by a factor
of up to 5 × 105 relative to unisite catalysis (Boyer, 1993,
1997; Gao et al., 2003).
6. How Are the Chemical Reactions (ATP Synthesis
and Hydrolysis) Modulated by the Essential
Residues in the Binding Pocket?
Specifically, how is hydrolysis of ATP prevented when
the affinity of the enzyme for ATP is reduced after its
synthesis, permitting release of ATP? From molecular
dynamics simulations, we show that the positions of
the catalytic residues change during the reaction cycle
and that they are no longer in a position to accelerate
the reaction when ATP is released.
Results and Discussion
Rotational Mechanism for Chemomechanical
Coupling (Questions 1 and 3)
Two molecular dynamics simulations (Ma et al., 2002;
Böckmann and Grubmüller, 2002) have provided important insights into the mechanism of F1-ATPase action.
Both calculations were performed with rotation of the γ
subunit enforced in the direction predicted for synthesis (see Itoh et al. [2004] and Diez et al. [2004] for an
experimental confirmation of this assumption). The
timescale for one rotation of the γ shaft is in the microsecond-to-millisecond range (Kinosita et al., 2004) and
is therefore not directly accessible to the nanosecond
timescales probed by standard molecular dynamics
simulations. To overcome this problem, the conformational transitions in F1-ATPase were obtained by molecular dynamics simulations in the presence of biasing
forces, which were applied to either the γ subunit alone
or the entire structure in a procedure that drives the
system from one state to the other without explicitly
constraining the nature of the transition path. The implicit assumption in such studies is that meaningful information concerning the mechanism can be obtained
even though the time scale of the forced rotational transition of the γ subunit is several orders of magnitude
faster than the actual rotation rate.
The simulation results demonstrate how the rotation
of the γ subunit induces the structural changes in the
catalytic β subunits and explain why there is much less
movement in the catalytically inactive α subunits that
are bound to ligand. Both van der Waals (steric) and
electrostatic interactions contribute to the coupling between the β and the γ subunits. The dominant electrostatic interactions occur between positive residues of
both the coiled-coil portion and the globular region of
the γ subunit (the “ionic track”) and the negatively
charged residues of the β subunits (see Figures 4 and
5 of Ma et al. [2002]). This ionic track leads to a smooth
rotation pathway without large jumps in the coupling
energy and is likely to contribute to the high efficiency
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of the chemomechanical energy transduction. The importance of some of the residues involved has been explored by mutation experiments (for a recent study,
which reviews some of the earlier data, see Greene and
Frasch [2003]). The simulations show how the rotation
of the γ subunit induces the opening motion of the β
subunits. In contrast, the closing motion of the β subunits appears to be spontaneous, once ligand is bound
to the active site and there are no steric interactions
caused by the γ subunit. This has been confirmed recently for an isolated β subunit in solution by nuclear
magnetic resonance (NMR) (Yagi et al., 2004). Interestingly, the conformational changes observed in the β
subunits have been shown to correspond to their lowest frequency normal modes (Cui et al., 2004). This implies that the structure of the protein is designed by
evolution such that the motions required for its function
can take place with a low energy cost.
Identification of Solution Binding Affinities with b
Subunit Conformations (Questions 2 and 3)
An essential element of the mechanism of F1-ATPase
action is the standard free-energy difference between
ATP, H2O, and ADP/Pi at the catalytic sites associated
with the different β subunit conformations. Four different binding constants for ATP have been measured
for F1-ATPase in solution. The values for the E. coli enzyme are 0.2 nM, 2 ␮M, 25 ␮M, and 5 mM, respectively
(Gao et al., 2003). It is generally agreed that the open
(βE) and half-closed (βHC) subunits have the two weakest binding sites and that the two other subunits (βTP
and βDP) contain the tightest site and the second highest affinity site. To determine the role played by each
of the β subunit conformations in the rotary-catalysis
mechanism of F1-ATPase, it was essential to resolve
the uncertainties concerning their binding affinities—
that is, to make a connection (the missing link) between
the microscopic (structural) and macroscopic (solution)
data. This has been achieved recently (Yang et al.,
2003, Gao et al., 2003) by combining free-energy difference simulations with experimental data. The freeenergy simulations were used to calculate the standard
free-energy change (⌬G0) of the hydrolysis reaction in
the various β subunit sites of the crystal structure. Freeenergy simulation techniques have been developed to
the stage where they can be used for answering quantitative questions in biomolecular systems (Simonson et
al., 2002). In the application of these techniques to F1ATPase, statistical errors had to be carefully controlled
to obtain reliable results (Yang et al., 2004). The bound
ATP/H2O was calculated as having a free energy similar
to that of ADP/Pi in the βTP site (1.5 kcal/mol), whereas
the free energy in the βDP site favors ADP/Pi relative to
ATP/H2O by 9 kcal/mol. Experiments have shown that
under unisite hydrolysis conditions (that is, at ATP concentrations so low that only one ATP is bound to the
enzyme), the free energies of ATP/H2O and ADP/ Pi in
the occupied site are nearly the same. The measured
⌬G0 value is 0.4 kcal/mol in the mitochondrial enzyme
and −0.6 in the E. coli enzyme. Because unisite hydrolysis is expected to take place in the site that has the
highest affinity for ATP, the simulation results can be
used to identify the βTP and βDP subunits as the ones
with the highest and second highest affinity for ATP,
respectively. The βE site, for which no calculations have
been made because of the absence of a bound ligand,
is identified as the site with a binding constant of 25
␮m (Gao et al., 2003). Free-energy simulation results,
based on βHC structure, agree with the values measured when the proton-motive force is present (Nakamoto et al., 2000). This indicates that βHC is responsible
for binding of the reactants ADP/Pi during ATP synthesis and release of products ADP/Pi during ATP hydrolysis. Having matched the ATP binding constants with
specific β subunit conformations, it was also possible
to determine the binding constants for ADP and Pi for
each of the β sites. This analysis also relied upon both
experimental data and free-energy simulations. A surprising finding was that the strong binding site for ADP/
Pi is the βDP site, in contrast to the strong binding site
for ATP and H2O, which is the βTP site (for details, see
Gao et al. [2003]).
From these results, it can be shown that there are
two major contributions to the driving force (actually a
biasing free energy) that rotates the γ subunit when ATP
is hydrolyzed by F1-ATPase (Gao et al., 2003). The first
contribution is the increase in the binding free energy
of ATP in going from the βE to the βTP state; this is in
agreement with the original model of Wang and Oster
(1998). However, the second contribution is a new result; it arises from the fact that, once hydrolysis takes
place and ADP/Pi occupies the binding site, the conformation is biased toward βDP.
Subunit Thermodynamics in ATP Synthesis
and Hydrolysis
In accordance with the E1E2 model, different conformations of the catalytic β subunits serve for substrate
binding and product release during ATP synthesis and
hydrolysis. Figure 3A shows the thermodynamic properties of the different conformations of the catalytic β
subunits involved in the ATP synthesis reaction, which
is driven by a clockwise rotation of the γ subunit (see
also Figure 4). The corresponding diagram for hydrolysis is shown in Figure 3B. The βHC subunit binds ADP/
Pi because ADP/Pi has a lower free energy in the βHC
subunit than in solution. Also, the rate of binding is expected to be relatively fast. The value for the ADP “on”
constant for E. coli F1-ATPase is about 106 M−1s−1 (Senior et al., 2002); however, that for Pi is not known. Because the potential of ATP in the βHC site is higher than
that in solution (see Figure 3A), there is little interference (inhibition) from ATP binding, even when it is present at a concentration similar to that of ADP/Pi. This
is one of the essential elements of the E1E2 model. Rotation of the γ subunit by 90°, after ADP and Pi are
bound (see Figure 4), transforms βHC into βDP. This conformational change does not induce synthesis because
the reaction free energy still strongly favors ADP/Pi (see
Figure 3A). A further rotation of 120° changes βDP to
βTP, the high-affinity site for ATP. The free energies of
bound ATP and ADP/Pi are approximately equal in βTP,
and synthesis can begin, but the rate is much slower
(0.04 s−1 in E. coli) than the observed maximal rate (10–
100 s−1 in E. coli) (Senior, 1992). A conformational
change is required to shift the equilibrium toward ATP
and increase the rate of ATP synthesis. Free-energy
simulations (Yang et al., 2003; W.Y., Y.Q.G., S. Boresch,
and M.K., unpublished data) suggest that this occurs
in a conformation similar to βTP but with local structural
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199
Figure 3. The Changing Chemical Potentials
of ATP and ADP/Pi in a β Subunit as a Function of γ Subunit Rotation
A full 360° cycle for a single catalytic subunit
is shown (see also Figure 4).
(A) ATP synthesis by the clockwise rotation
of the γ subunit. The rotation angle of the γ
subunit is indicated on the abscissa, and the
corresponding β subunit conformations are
shown. In addition to the known structures,
an intermediate state, βTP*, favoring ATP, is
shown between βTP and βE sites (see text).
Orange is used for ATP and green for ADP/
Pi. The thermodynamically favored states are
represented by filled circles and the unfavored states by open circles. The dominant
transitions are represented by solid arrows
and the unimportant ones by dotted arrows.
The chemical reaction is indicated by arrows
that are half solid green (ADP/Pi) and half
solid orange (ATP). The solution state of ATP
is represented by an orange line at 11.3 kcal/
mol (the potential of ATP relative to ADP/Pi
at cellular concentrations; see text), and the
solution state of ADP/Pi is represented by a
green line, which is set to zero.
(B) ATP hydrolysis, which results in the counterclockwise rotation of the γ subunit. The rotation angle of the γ subunit is indicated on the
abscissa, and the corresponding β subunit
conformations are shown. In addition to the
known structures, an intermediate state, β*,
favoring ADP/Pi, is shown to represent
where ATP hydrolysis is likely to occur under
normal conditions. Orange is used for ATP
and green for ADP/Pi. The thermodynamically favored states are represented by filled
circles and the unfavored states by open circles; the dominant transitions are represented by solid arrows and the unimportant
ones by dotted arrows. The chemical reaction is indicated by arrows that are half solid
green (ADP/Pi) and half solid orange (ATP).
The solution state of ATP is represented by
an orange line at 11.3 kcal/mol (the potential
of ATP relative to ADP/Pi at cellular concentrations; see text), and the solution state of
ADP/Pi is represented by a green line, which
is set to zero.
changes induced by rotation of the γ subunit to about
300°; we refer to this structure, which has not been observed experimentally, as βTP* (Figure 3A). Rotation of
the γ subunit to complete the 360° cycle (Figure 3A)
creates the βE site, which binds to ATP less strongly, as
required for product release (Antes et al., 2003). As the
βE site is approached, the free energy of ATP becomes
higher than that of ADP/Pi. A lower value of the free
energy of ATP in the βE site, relative to that in solution,
is required for optimization of hydrolysis, as well as
synthesis, because βE is the binding site for the ATP
substrate in hydrolysis, (see Figure 4), as well as the
release site for ATP after synthesis. The openness of
the βE site makes the release and binding rate of ATP
rapid enough such that it is not rate limiting under normal conditions (see below).
Figure 3B shows the thermodynamics properties of
the different conformations of the catalytic β subunits
in ATP hydrolysis, which correspond to a counterclockwise rotation of the γ subunit from right (360°) to left (0°)
on the abscissa. The βE site binds ATP more strongly
than in solution at the beginning of the rotation cycle,
which can prevent the interference of ADP/Pi. Tighter
binding of ATP to the βTP site provides a driving force
for γ subunit rotation. Rotation of the γ subunit transforms the βE site in E1 to the βTP site in E2. The free
energies of bound ATP and ADP/Pi are approximately
equal in βTP. Hydrolysis can start at this position, but
the rate is much smaller (about w0.1 s−1, in E. coli) than
the maximum overall hydrolysis rate (60–80 s−1, in
E. coli). Another 120° γ subunit rotation, mainly driven
by ATP binding to another site, causes the transition
βTP / βDP, during which the potential for ATP increases
and that for ADP/ Pi decreases. Because the βDP site
strongly favors ADP/Pi relative to ATP/H2O and the
active-site residues are appropriately positioned for ca-
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200
Figure 4. Schematic Diagram Illustrating the Trisite E1E2 Model for ATP Synthesis and Hydrolysis by F1-ATPase
The figure shows a 120° rotation cycle for the molecule, which corresponds to the synthesis or hydrolysis of one ATP. The catalytic binding
sites are labeled according to their structural descriptions (βE, βTP, βDP, and βHC) (Abrahams et al., 1994; Menz et al., 2001) and indicated by
various shapes similar to those used in the literature (Braig et al., 2000). ATP is orange and ADP/Pi is green (Pi = H2PO4−). The sequence of
events for ATP synthesis is shown by red arrows, whereas blue arrows indicate the sequence for ATP hydrolysis. The constant kx is the
binding rate constant for species x at a given binding site, and k−x is the corresponding dissociation rate constant. ks#, kh#, ks, and kh are
rate constants for the indicated rotations. For hydrolysis, the present scheme is in general agreement with the proposals of Senior et al.
(2002) and Kagawa et al. (2004) (see also Supplemental Data).
talysis, hydrolysis is expected to occur during the βTPto-βDP transition (Gao et al., 2003). Thus, because of
the relative binding energies—ATP binding is strongest
in the βTP site, whereas ADP/Pi binding is strongest in
the βDP site (Gao et al., 2003)—the transition of βE /
βTP involving ATP binding and the transition of βTP /
βDP involving ATP hydrolysis contribute most of the energy that drives the rotation of γ subunit (Karplus and
Gao, 2004; Gao et al., 2003). In the transition of βDP
/ βHC, the overall binding affinity for ADP/Pi changes
moderately, but the ADP binding affinity is lowered by
about 3.7 kcal/mol, and the Pi binding affinity is increased by about the same amount. This suggests that
ADP is released first, followed by Pi. This unbinding sequence is supported by inhibition measurement (see
the Supplemental Data available with this article online). The release of Pi, which, when bound, constrains
the system in E2 (with the βHC conformation), permits a
30° γ subunit rotation to transform the structure to E1
(with βHC / βE) and complete the 360° cycle (see Figure 3B). The 30° rotation is driven by energy that we
suggest is stored in the twisted γ subunit during ATP
binding in hydrolysis (W.Y., Y.Q.G., S. Boresch, and
M.K., unpublished data). Because of the high binding
affinity of the βHC site for Pi, the release of Pi is the
rate-limiting step at high ATP concentration; this is a
necessary aspect of efficient ATP synthesis, as indicated above.
Model for Complete F1-ATPase Catalytic Cycle
(Questions 3 and 4)
The catalytic cycle for ATP synthesis and hydrolysis by
F1-ATPase is illustrated in Figure 4. Two different conformations of F1-ATPase participate in the reaction cycle, in formal analogy to the E1E2 model (DeMeis and
Vianna, 1979). As a result, there are different binding
sites for the substrates in ATP synthesis (ADP/Pi) and
hydrolysis (ATP) and for the products (ATP and ADP/
Pi, respectively). Experimental binding data and freeenergy simulations (Yang et al., 2003) suggest that
structure E1 has the subunit conformations βTP, βDP,
and βE (Abrahams et al., 1994), whereas E2 consists of
βTP, βDP, and βHC (Menz et al., 2001) (Figure 1). The two
rotation steps (30° and 90°) shown in Figure 4 correspond to those in single-molecule hydrolysis experiments (Yasuda et al., 2001) and are assumed to occur
in synthesis. As of yet, there is no direct evidence for
this assumption. The ATP synthesis reaction begins
with a γ subunit rotation of approximately 30° due to
the proton motive force acting on the F1 moiety through
the Fo complex (Diez et al., 2004) or, equivalently, an
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201
external force (Itoh et al., 2004), changing E1 to E2 and,
most importantly, βE / βHC. (Menz et al., 2001). Binding
of the substrates Pi and ADP to the βHC subunit takes
place without rotation. Once the substrates are bound,
a 90° rotation occurs, which changes E2 to E1. ATP synthesis occurs during this step and is followed by product release from βE. In ATP hydrolysis, the ATP substrate binds to the βE subunit of E1 and the hydrolysis
products are released from the βHC subunit of E2. The
ATP hydrolysis reaction occurs in a conformation between that of the βTP and βDP sites. The rotation of the
γ subunit is produced by the differential binding of ATP
and ADP/Pi to the various subunit conformations, as
described above (Boyer, 1997; Senior et al., 2002; Karplus and Gao, 2004).
The total free energy of ATP hydrolysis or synthesis
can be divided into five components (Figure 4). They
are the binding free energy of ATP (−⌬GT = RTln(kT
[ATP]/k−T)); two free-energy changes, denoted hereafter
as W1 and W2, associated with the rotation of the γ subunit; and the free energies associated with release
of ADP (−⌬GD = RTln(k−D/kD[ADP])) and Pi (−⌬GP =
RTln(k−P/kP [Pi])). For definitions of the symbols, see the
legend of Figure 4. Because the free-energy components W1 and W2 are associated with the γ subunit rotation, they are functions of the external load. The freeenergy change for ATP hydrolysis in the absence of an
external load can be written as
⌬Gsol = W1 + W2 + ⌬GT − ⌬GD − ⌬GP,
(2)
where kB is the Boltzmann constant and T is the temperature. When an external load Fext(θ) is applied to the
system via the γ subunit (as by, for example, the protonmotive force), an additional term has to be introduced
into Equation 1. The integration range for the rotation
of the γ subunit per ATP hydrolyzed or synthesized
is 0° to 120°. In the case of proton transport,
∫0120Fext(q)d(q) = n⌬mH+, where n is the number of protons
transported across the inner membrane of the mitochondrion per ATP hydrolyzed (synthesized) and
DmH+ is the proton free-energy gradient. The existing
experimental data indicate that n = 4 (Senior et al.,
2002; Karplus and Gao, 2004), although the exact value
is a still a matter of debate. Accordingly, W = W1 + W2,
the total free-energy change corresponding to the elementary step (120° rotation of the γ subunit) in the presence of an external force, can be written as
W = W1 + W2
∫
= ⌬Gsol − ⌬GT + ⌬GD + ⌬GP + Fext(q)dq.
d[E1T]/dt = kT[E1][T] + ks[E2DP] − (k−T + kh)[E1T],
(3)
(4)
d[E2DP]/dt
= kD[E2P][D] + kh[E1T] − (k−D + ks)[E2DP],
(5)
d[E2P]/dt
= kP[P][E2] + k−D[E2DP] − (k−P + kD[D])[E2P],
(6)
(1)
where ⌬Gsol is the free energy of ATP hydrolysis in solution. At concentrations of 1 M for ATP, ADP, and Pi,
⌬Gsol = −7.3 kcal/mol (Stryer, 1995), whereas at cellular
concentrations, the value is −12.3 kcal/mol for human
cells and −11.3 kcal/mol for E. coli (Nelson and Cox,
2000). From Figure 4, the rate constants for the rotation
of the γ subunit kh, ks and k#h, k#s are related through
the free-energy changes W1 and W2, respectively,
k′h
kh
= e−W1/kBT,
= e−W2/kBT,
ks
k′s
Because the concentration dependence (−ln[ATP]/
[ADP][Pi]) in ⌬Gsol cancels exactly with that in ⌬GT, ⌬GD,
and ⌬GP, W is independent of the solution concentrations of ATP, ADP, or Pi, as it should be. The binding
and dissociation rate constants of the substrates ATP
and ADP have been obtained from experimental measurements such as the fluorescence quenching experiments of Weber and Senior (1997) for the E. coli system. The rate constants kh, ks and k#h, k#s represent the
rate of rotation of the γ subunit of the F1-ATPase in Figure 4 and can be measured by single-molecule experiments (Yasuda et al., 2001).
Kinetic Analysis of ATP Synthesis and Hydrolysis
by F1-ATPase (Questions 4 and 5)
In the following, we use the model given in Figure 4
to estimate important kinetic properties of F1-ATPase,
including the ATP, ADP, and Pi concentration dependence of the ATP hydrolysis and synthesis rates. We
show quantitatively how ATP hydrolysis and synthesis
are both optimized and regulated given the cellular
concentrations of ATP, ADP and Pi, thereby providing
an answer to question 5 from the introduction.
The kinetic equations corresponding to the model
shown in Figure 4 have the form
d[E1]/dt = k−T[E1T] + k′h [E2]− (k′s + k1[T])[E1], (7)
d[E2]/dt = k′s[E1] + k−P[E2] − (kP[P] + k′h)[E2],
(8)
[E1] + [E2] + [E2DP] + [E1T] + [E2P] = [E0],
(9)
and
where [E0] is the total concentration of the FoF1-ATP
synthase.
The steady-state approximation is applied to Equations 4–8 corresponding to the species in Figure 4, under conditions where the frictional load is small and the
reaction is heavily biased toward either ATP hydrolysis
or synthesis direction such that the binding of reactants
or the release of products (but not the rotation of the γ
subunit) is the rate-limiting step. The inverse rate of
ATP synthesis is given by
(
1
k−P
1
=
1+
Vsyn
kD[D]
kP[P]
)
+
1
1
1 kT[T]
+
+
kP[P] k−T k′s k−T
(10)
and that for ATP hydrolysis by
(
)
1
1
1
kD[D]
1
+
=
+
1+
Vhyd
kT[T] k−D k−P
k−D
+
(
)
1 kP[P]
kD[D]
1 +
.
k′h k−P
k−D
(11)
Cell
202
Figure 5. The Dependence of the Kinetic Parameters for ATP Synthesis upon Product Concentrations
The [ATP] concentration is in units of 1 M. Red curves show the predictions for (A)
, (B) KM(Pi), and (C) KM(ADP). In (A), experimental
values (with error estimates) are shown; the blue spot represents the value for [ATP] equal to zero. In (B), the embedded figure shows
calculated and experimental results for the rates of ATP synthesis at various Pi concentrations when the ADP concentration is 0.75 mM. In
(C), the embedded figure shows calculated and experimental results for the rates of ATP synthesis at various ADP concentrations when the
Pi concentration is 10.0 mM. The data were provided by R.K. Nakamoto (Al-Shawi et al., 1997).
For definitions of the symbols in Equations 10 and
11, see Figure 4 and the caption of Figure 5.
The direction and rate of the reaction are primarily
determined by the magnitude of the proton-motive
force. This property of the E1E2 mechanism is essential
for an enzyme like FoF1-ATP synthase, which works in
both directions with high efficiency. In other words, ATP
and ADP/Pi do not compete for binding at the same
binding site, such that the inhibition due to binding of
the products to the reactant binding sites is avoided
in both ATP hydrolysis and synthesis. As a result, the
presence of high concentrations of ATP in the solution
does not suppress ATP synthesis (see below for the
inhibition constant of ATP).
Equations 10 and 11 permit one to estimate the important kinetic parameters, such as the maximum ATP
synthesis rate, the Michaelis-Menten constants, KM of
the reactants (the concentration of the reactant at
which the reaction rate is half of its maximum value),
and the inhibition constants of the products. They are
analyzed in the Supplemental Data. For example, from
Equation 10, the maximum ATP synthesis rate, corresponding to [D],[P] / N and [T] / 0, is k−T = KTkT,
where KT and kT are the dissociation constant and the
binding rate constant of ATP to the βE site. KT and kT
were shown to be about 25 ␮M and 2 × 106 M−1s−1
(Senior et al., 2002), and thus the maximum ATP synthesis rate is about 50 s-1, consistent with the experimental
values of 60–80 s−1 (Boyer, 1997; Senior et al., 2002). In
the presence of high concentrations of Pi, Equation 10
also provides an approximate relation between the Michaelis-Menten constant KM(ADP) for ADP and the
maximum ATP synthesis rate
max
= KM(ADP)kD.
Vsyn
(12)
Because the maximum ATP synthesis rate is about
50 s−1 (as shown above) and the experimental value of
KM(ADP) is about 25 ␮M, the kD is estimated to be 2 ×
106 M−1s−1, close to the experimental value of 5 × 105
M−1s−1. Using a similar equation for Pi, one can deter-
mine that the Pi binding rate constant is about 2 × 104
M−1s−1. A 120° rotation of the γ subunit during ATP hydrolysis in the absence of the proton-motive force and
under a small frictional load was shown to take about
0.2 ms (Yasuda et al., 2001). Assuming that the speed
of the γ subunit is the same during the two substeps of
rotation, it can be estimated that kh# is about 1.5 ×
104 s−1 (Yasuda et al., 2001; Supplemental Data). Using
this value of kh# and the binding rate constant of ADP
and Pi, the inhibition of ADP and Pi on the ATP hydrolysis reaction can be estimated via Equation 11. At negligible ADP concentrations, the inhibition concentration
of Pi, Ki(Pi), at which the ATP hydrolysis rate is one half
of its maximum value, is about 900 mM and agrees with
the experimental lower limit of 10 mM obtained by Senior and coworkers (Nadanaciva et al., 1999) and also
an estimated value of 10 M for E. coli F1-ATPase by
R.K. Nakamoto and coworkers (personal communication). Similarly, at low Pi concentrations, the Ki(ADP) is
shown to be 30 ␮M, again in agreement with the experiments (<100 ␮M). If a value of 1.5 × 104 s−1 is also used
for the rotation of the γ subunit in the reverse direction
but under conditions where there is a very large protonmotive force and the reaction is predominantly in the
ATP synthesis direction, Equation 10 can be used to
estimate the inhibition concentration of ATP, Ki(ATP), at
which the maximum rate of ATP synthesis is one half of
its value. From Equation 10, Ki(ATP) is estimated to be
7.5 mM, whereas the experimental value is 5 mM.
The calculated kinetic parameters and the available
experimental results are listed in Table 1. Figure 5
shows the maximum rate of ATP synthesis and the KM
values for ADP and Pi, respectively, as a function of ATP
concentration. All products (ATP in synthesis and ADP/
Pi in hydrolysis) inhibit the reaction. Consequently, the
higher the concentration or concentrations of the product or products, the smaller the maximum rate constant
(see Figure 5 and Supplemental Data). Importantly, the
KM values of the reactants also decrease when the solution concentration of the products increases. This result is an essential property of the enzyme, which
Theory
203
Table 1. Kinetic Parameters
Exp.
Est.
V max
syn
kD
Ki (Pi)
Ki (ADP)
Ki (ATP)
60–80 s−1
50 s−1
5 × 105 M−1s−1
2 × 106 M−1s−1
>10 mM
900 mM
<100 ␮M
30 ␮M
5 mM
7.5 mM
Maximum rate V max
syn for ATP synthesis, ADP binding rate constant kD, and inhibition constant Ki of Pi, ADP, and ATP. Ki (ADP) and Ki(Pi) are
the concentrations of ADP and Pi when the rate of ATP hydrolysis takes one-half of its maximum value (at saturating conentrations of ATP),
and Ki (ATP) is the concentration of ATP at which ATP synthesis takes one-half of its maximum value (at saturating concentrations of ADP
and Pi). The method used to determine the parameters is described in the main text.
makes the KM value of each ligand (ATP, ADP, and Pi;
see below) low enough such that the maximum rates of
both ATP hydrolysis and synthesis can be achieved.
In contrast to the E1E2 mechanism proposed here,
competitive binding between the reactant and product
at the same binding site would allow at most only one
of the two reactions to achieve a maximum rate constant at any given concentrations of ligands. Such a
mechanism would not serve the biological function of
FoF1-ATP synthase, nor does it agree with the experimental observations. Experiments show that the KM
values for ADP and Pi (29 ␮M and 1 mM) in ATP synthesis and the KM value for ATP (25 ␮M) in hydrolysis are all
lower than their cellular concentrations. As discussed
above (see Table 1), the present model gives inhibition
concentrations for both ATP hydrolysis and synthesis
that are consistent with the experimental results. From
the analysis, it also follows that, at cellular conditions,
only ADP plays a significant role in regulating the function of the enzyme through product inhibition, which is
consistent with experimental observations (Nicholls
and Ferguson, 2002). The ATP and Pi cellular concentrations are lower than their inhibition concentrations
and thus are much less important. The different role of
ADP from that of ATP and Pi is consistent with the fact
that ADP has a concentration more than ten times
lower than that of either ATP and Pi, and thus its change
leads to the sensitive regulation of the enzymatic activity and has only minor influence on the concentrations
of the other two.
The kinetic model leads to results that can be tested
by experiments (see also Supplemental Data). It is predicted that the Michaelis-Menten constants for ADP
and Pi decrease with increasing ATP concentration (as
max
/KM(Pi) is indepenshown in Figure 5), such that V syn
dent of ATP concentration at any given ADP concenmax
/KM(ADP). These predicted results
tration, as is V syn
are consistent with the experiments of Grubmeyer
et al. (1982), which showed that, for ATP synthesis,
max
/KM(ADP) is a constant. The model predicts a
V syn
value of about 104 M−1s−1 for the important binding rate
constant of Pi of E. coli F1-ATPase, which has not been
measured. Also, the model predicts the occupancy of
various sites as a function of the reactant concentrations, which are not yet known experimentally. With the
recent demonstration that F1-ATPase can synthesize
ATP (Itoh et al., 2004), more data are likely to become
available to provide additional tests.
Structural Basis of Thermodynamics and Kinetics
(Questions 3 and 6)
Simulation studies also allow us to understand how
essential residues modulate the chemical reactions in
the binding sites. The sensitivity of the reaction free energy to small displacements of the large number of
charged residues in the active site is one of the key
features of the catalytic β subunits of F1-ATPase. The
small difference between the very similar structures of
the βTP and βDP sites has been shown by free-energy
simulations to result in a difference in the hydrolysis
reaction free energy of 9 kcal/mol, with residues
αArg373 and βArg189 making the most important contribution (Yang et al., 2003).
Figure 2 shows the key residues in the βDP site with
ATP bound. Residue αArg373, which is the only α subunit residue contributing to the β subunit catalytic site,
has been suggested (Senior et al., 2002; Menz et al.,
2001; Dittrich et al., 2004) to play a role in F1-ATPase
hydrolysis analogous to the so-called “arginine finger”
in GTPases (Rittinger et al., 1997). Structural studies
have shown that αArg373 can be at a distance of 10 Å
from the phosphate in the βTP site (Gibbons et al., 2000,
Kagawa et al., 2004), in contrast to its position in other
structures (Abrahams et al., 1994; Braig et al., 2000;
Menz et al., 2001). Also, if αArg373 is mutated, hydrolysis is slowed down significantly and synthesis is eliminated (Senior et al., 2002). Calculations of ATP unbinding from the catalytic site confirm that αArg373 moves
away when ATP is no longer present and that αArg373
is essential for biasing the reaction free energy in the
direction of hydrolysis and at the same time lowers the
activation barrier (Yang et al., 2003; W.Y., Y.Q.G., S.
Boresch, and M.K., unpublished data). Conversely, a
displacement of αArg373 from the active site by a conformational change due to rotation of the γ subunit
(from βTP to βTP*, as suggested in Figure 3A) shifts the
thermodynamic potential so as to favor ATP synthesis.
Residue βArg189, whose equivalent is not present in
GTPases, has been found to be important for ATP synthesis (Boyer, 1997; Senior et al., 2002). Overall, the Arg
pair (αArg373 and βArg189) and their relative positioning appear to make the major contribution to switching
between hydrolysis and synthesis. Structural studies
(Kagawa et al., 2004) and simulations suggest that
αArg373 acts to “transmit conformational signals across
the α/β subunit catalytic interface” (Nadanaciva et al.,
1999) as part of the chemomechanical coupling to the
γ subunit. Calculations indicate that in a model for βTP*,
residue βGlu188 is in approximately the same position
relative to the ATP γ-phosphate group as in the βTP
structures (Abrahams et al., 1994, Menz et al., 2001). It
can polarize the water molecule that is involved in the
synthesis reaction in βTP* and in the hydrolysis reaction
in βDP. Together with βGlu188, other residues such as
βLys162 are essential for the catalysis of synthesis and
Cell
204
hydrolysis. Small displacements of these residues can
significantly change the reaction rate. For instance,
during ATP synthesis, after the formation of ATP at the
βTP* site, the displacements of catalytic residues appear to prevent ATP with high chemical potential from
being hydrolyzed to ADP/Pi, suggesting kinetic rather
thermodynamic control. The mutation of charged residues not in direct contact with the ligand, such as
βArg246, has been shown recently to lead to the loss
of activity (Ahmad and Senior, 2004). This is indicative
of the intricacy of the structure of the catalytic region
of the β subunits, which is required to fulfill the multiple
functions of regulating absolute binding, relative binding, chemical catalysis, and conformational change.
Conclusion
A detailed mechanism for ATP synthesis and hydrolysis
has been proposed on the basis of molecular dynamics
simulations; kinetic modeling; and experimental structural, thermodynamic, and kinetic data. The model,
which represents the first consistent description of how
this bifunctional enzyme is able to perform both ATP
synthesis and ATP hydrolysis, requires further tests. We
hope that publication of the model will stimulate experimental work, as well as additional theoretical studies,
to substantiate or refine the present proposal.
Supplemental Data
Supplemental Data include supplemental text, Supplemental References, and one figure and can be found with this article online at
http://www.cell.com/cgi/content/full/123/2/195/DC1/.
Acknowledgments
We thank J.E. Walker for providing a preprint of Menz et al. (2001)
prior to publication, R.K. Nakamoto and M.K. Al-Shawi for supplying the experimental data shown in Figure 5B, and A.E. Senior for
the permission to use Figure 1. We thank J. Kuriyan for his many
suggestions, which considerably improved the manuscript, and
R.K. Nakamoto and A. Horwich for their comments. During development of the present model, we have learned much about this
wonderful enzyme from A.G.W. Leslie, A.E. Senior, and J.E. Walker.
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